Final answer:
The skateboard will move backward at a speed of approximately 0.63 m/s when the 50-kg boy steps off the front at a speed of 0.5 m/s, by applying the principle of conservation of momentum.
Step-by-step explanation:
The subject of the student's question is Physics, specifically involving momentum conservation and Newton's laws. The grade level is likely High School, where students begin to learn about these concepts in more depth. To answer the question, we'll apply the principle of conservation of momentum, which states that the total momentum of a system remains constant if no external forces are acting on the system. The momentum before the boy steps off will equal the momentum after he steps off. Here, the system consists of the boy and the skateboard.
Momentum is calculated by multiplying mass (m) by velocity (v). Before the boy steps off the skateboard, the total momentum is 0 because both are at rest. After the boy steps off:
p_{boy} = m_{boy} imes v_{boy}
p_{skateboard} = m_{skateboard} imes v_{skateboard}
Since the total momentum must remain 0, we have:
m_{boy} imes v_{boy} = - m_{skateboard} imes v_{skateboard}
Plugging in the values gives us:
50 kg imes 0.5 m/s = - 2.26 kg imes v_{skateboard}
Now we can solve for v_{skateboard}:
v_{skateboard} = - (50 kg imes 0.5 m/s) / 2.26 kg
v_{skateboard} = - 11.05 m/s / 2.26 kg
v_{skateboard} ≈ -0.63 m/s
The negative sign indicates the skateboard moves in the opposite direction to the boy's step. The correct answer is B) 0.63 m/s.